Seeing that there is a Mastery skill that starts you with 50 extra gold, it would most likely be under powered. Because if the match moves into late game, you will be at a slighter disadvantage than, say, someone with 3G/10s. Lets do the simple math real fast:

//3 Quints of GP per 10
Every 10 seconds, you receive 3 gold. That calculates to 1 gold about every 3.3 seconds.

//3 Quints of GP per 10 Breakdown
1 gold at every 3.3 seconds of the game. Let's go with the 20 minute mark. 20 minutes is a total of 1200 seconds. We then divide 1200 by 3.3 (1200/3.3:1), which gives us 363.6. So, After the 20 minute mark we will have over 300 gold. Now, if we look at the 10 minute mark, all we need to do is divide by 2 ((1200/2)/3.3):1, which gives us 181.8 gold at the 10 minute mark. And of course, cutting it down against, half the time would be half the gold giving us 91 gold.

//3 Quints of Starting GP at 25
Start the match with an extra 75 gold.

Let's say these new quints give an extra 25 gold each at the start (75 gold total). The GP/10s would out pace these Quints at around the 4 minute mark.

Now, one thing to keep in mind though, having the extra gold might help your AD off to a good start, but I still feel they would be completely underpowered (unless my math is way off).

Interesting idea but I think the only thing it'd accomplish is make the first 2-3 minutes of the game more passive (not that this would be a bad thing). In a team scenario it would mean more wards which causes the first route of the jungler to be mapped out, or it would create 1-2 more pots in laning phase so the tactic of bursting someone at level 2-3 not to kill but to force them out of lane would be delayed until around level 5 after you force someone to use those extra pots with harass.

I guess it wouldn't be overpowered in the sense that you would basically be trading mid-game power from other quints for the early game. I could see solo lane tanks/fighters and junglers using it, but even then it feels more like a niche pick in the jungle than anything. Movement speed for tank junglers is huge as it gives them that power for the entire game, and AD for fighter junglers helps them clear camps faster, which means less damage taken and less of a need for those extra pots. Maybe it helps with some mage junglers like Diana since she has long cooldowns so running AP quints won't make that much of an impact in the first few camps? I think marksmen/mages/assassins will stick with their current quints. It would be interesting to see what supports would do if it was +25 gold per quint... frontload your gold for that extra ward in the enemy jungle, or stick with the steady income of gp5 for a free ward every 125 seconds earlier (or earlier sightstone/philo stone for an even stronger passive gold income). Personally I'm all about long term investments so I'd stick with GP5 quints.

The one thing I'd keep an eye on is how much more powerful it would make builds that start with a flask, since that item was extremely powerful before the gold cost was increased.

TL;DR - interesting idea but not sure it would see much use in the current state of the game.